Dynamic modeling of a finite volume of solid oxide fuel cell: The effect of transport dynamics

A dynamic model for a finite volume of cell based on physical principles is built in the form of a nonlinear state-space model to investigate dynamic behaviors of tubular solid oxide fuel cell (SOFC) and develop a control relevant model for further control studies. Dynamic effects induced by diffusions, intrinsic impedance, fluid dynamics, heat exchange and direct internal reforming/shifting (DIR) reactions are all considered. Cell temperature, ingredient mole fractions, etc. are the state variables and their dynamics are investigated. Dynamic responses of each variable when the external load changes are simulated. Simulation results show that fuel flow, inlet pressure and temperature have significant effects on the dynamic performance of SOFC. Further it is shown that, compared to other inlet flow properties, cathode side air inlet temperature has the most significant effect on SOFC solid phase temperature and performance. Compared with inlet pressures and temperatures, the effect of flow velocity is not significant. Simulation also indicates that the transient response of SOFC is controlled mainly by the dynamics of cell temperature owing to its large heat capacity.     

Comparison of two IT DIR-SOFC models: Impact of variable thermodynamic, physical, and flow properties. Steady-state and dynamic analysis

This paper compares two dynamic, one-dimensional models of a planar anode-supported intermediate temperature (IT) direct internal reforming (DIR) solid oxide fuel cell (SOFC): one where the flow properties (pressure, gas stream densities, heat capacities, thermal conductivities, and viscosity) and gas velocities are taken as constant throughout the system, based on inlet conditions, and one where this assumption is removed to focus on the effect of considering the variation of local flow properties on the prediction of the fuel cell performance. The refined model consists of mass, energy, and momentum balances, and of an electrochemical model that relates the fuel and air gas compositions and temperatures to voltage, current density, and other relevant fuel cell variables. Simulations for steady-state and dynamic conditions have been carried out and the results obtained from the two models compared. For a co-flow SOFC operating on a 10% pre-reformed methane fuel mixture, with 75% fuel utilisation, inlet fuel and air temperatures of 1023 K, average current density of , and an air ratio of 8.5, the results show that, although the error incurred in the prediction of the flow properties in the first model is significant, there is good agreement between both models in terms of the overall cell performance: the maximum difference in the local temperature values is about 7 K and the cell efficiency differs by less than 1%. However, the discrepancies between the two models increase, especially in the fuel channel, when higher current density values are assigned to the cell.     

平板式直接内重整固体氧化物燃料电池的一维动态建模与仿真

This article aims to investigate the transient behavior of a planar direct internal reforming solid oxide fuel cell (DIR-SOFC) comprehensively. A one-dimensional dynamic model of a planar DIR-SOFC is first developed based on mass and energy balances, and electrochemical principles. Further, a solution strategy is presented to solve the model, and the International Energy Agency (IEA) benchmark test is used to validate the model. Then, through model-based simulations, the steady-state performance of a co-flow planar DIR-SOFC under specified initial operating conditions and its dynamic response to introduced operating parameter disturbances are studied. The dynamic responses of important SOFC variables, such as cell temperature, current density, and cell voltage are all investigated when the SOFC is subjected to the step-changes in various operating parameters including both the load current and the inlet fuel and air flow rates. The results indicate that the rapid dynamics of the current density and the cell voltage are mainly influenced by the gas composition, particularly the H2 molar fraction in anode gas channels, while their slow dynamics are both dominated by the SOLID (including the PEN and interconnects) tem-perature. As the load current increases, the SOLID temperature and the maximum SOLID temperature gradient both increase, and thereby, the cell breakdown is apt to occur because of excessive thermal stresses. Changing the inlet fuel flow rate might lead to the change in the anode gas composition and the consequent change in the current den-sity distribution and cell voltage. The inlet air flow rate has a great impact on the cell temperature distribution along the cell, and thus, is a suitable manipulated variable to control the cell temperature.     

Investigation on Flow Distribution in an External Manifold SOFC Stack by Computational Fluid Dynamics Technique

In this study, the flow distribution in a planar solid oxide fuel cell (SOFC) stack with external manifolds is investigated by computational fluid dynamics (CFD) technique. Three dimensional external manifold models are constructed for a SOFC stack composed of 24 cells. CFD simulations with air as operating gas are implemented for two types of stacks with different inlet manifolds, including the manifold with three tube inlets (T‐manifold) and the manifold with a gas chamber on top (C‐manifold). The influences of different parameters such as channel resistance and gas feeding rate on flow distribution are studied. Modeling results indicate that the increase of channel resistance and a lower gas feeding rate can respectively improve the uniformity factor of T‐manifold and C‐manifold from 0.963 to 0.995 and 0.989 to 0.998. For a given channel resistance, the pressure distribution in the inlet manifold plays a dominant role in the flow distribution. In addition, flow distribution in the stack with C‐manifold is generally more uniform than the stack with T‐manifold. Furthermore, flow characteristics of the two type inlet manifolds are investigated by measuring velocity distribution of the gas at manifold outlets using a hot‐wire anemometer.     

Solid oxide fuel cell reactor analysis and optimisation through a novel multi-scale modelling strategy

The simulation of a solid oxide fuel cell (SOFC) that incorporates a detailed user-developed model was performed within the commercial flowsheet simulator Aspen Plus. It allows modification of the SOFC's governing equations, as well as the configuration of the cell's fuel-air flow pattern at the flowsheet level. Initially, the dynamic behaviour of single compartment of a cell was examined with a 0D model, which became the building block for more complex SOFC configurations. Secondly, a sensitivity analysis was performed at the channel (1D) scale for different flow patterns. Thirdly, the effect of fuel and air flow rates on the predominant distributed variables of a cell was tested on a 2D assembly. Finally, an optimisation study was carried out on the 2D cell, leading to a robust, optimal air distribution profile that minimises the internal temperature gradient. This work forms the foundation of future stack and system scale studies.     

Modeling of a Tubular‐SOFC: The Effect of the Thermal Radiation of Fuel Components and CO Participating in the Electrochemical Process

A mathematical model based on first principles is developed to study the effect of heat and electrochemical phenomena on a tubul solid oxide fuel cell (SOFC). The model accounts fordiffusion, inherent impedance, transport (momentum, heat and mass transfer) processes, internal reforming/shifting reaction, electrochemical processes, and potential losses (activation, concentration, and ohmic losses). Thermal radiation of fuel gaseous components is considered in detail in this work in contrast to other reported work in the literature. The effect of thermal radiation on SOFC performance is shown by comparing with a model without this factor. Simulation results indicate that at higher inlet fuel flow pressures and also larger SOFC lengths the effect of thermal radiation on SOFC temperature becomes more significant. In this study, the H₂ and CO oxidation is also studied and the effect of CO oxidation on SOFC performance is reported. The results show that the model which accounts for the electrochemical reaction ofCO results in better SOFC performance than other reported models. This work also reveals that at low inlet fuel flow pressures the CO and H₂ electrochemical reactions are competitive and significantly dependent on the CO/H₂ ratio inside the triple phase boundary.     

Alternative concept for SOFC with direct internal reforming operation: Benefits from inserting catalyst rod

Mathematical models of direct internal reforming solid oxide fuel cell (DIR‐SOFC) fueled by methane are developed using COMSOL® software. The benefits of inserting Ni‐catalyst rod in the middle of tubular‐SOFC are simulated and compared to conventional DIR‐SOFC. It reveals that DIR‐SOFC with inserted catalyst provides smoother temperature gradient along the system and gains higher power density and electrochemical efficiency with less carbon deposition. Sensitivity analyses are performed. By increasing inlet fuel flow rate, the temperature gradient and power density improve, but less electrical efficiency with higher carbon deposition is predicted. The feed with low inlet steam/carbon ratio enhances good system performances but also results in high potential for carbon formation; this gains great benefit of DIR‐SOFC with inserted catalyst because the rate of carbon deposition is remarkably low. Compared between counter‐ and co‐flow patterns, the latter provides smoother temperature distribution with higher efficiency; thus, it is the better option for practical applications. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Analysis of a solid oxide fuel cell system for combined heat and power applications under non-nominal conditions

In this paper, a model for a solid oxide fuel cell (SOFC) system for decentralized electricity production is developed and studied. The proposed system, operated on natural gas, consists of a planar anode supported fuel cell section and a balance of plant (BoP) which includes gases supply, a fuel processor, a heat management system, an after-burner and a power conditioning system. A reference case is defined and evaluated taking into account the state of the art of the technology and the related technical constrains. Electrical and thermal efficiency of the system, for non-reference conditions are evaluated. In particular, the effect of the deviation from the reference conditions of fuel utilization, gas temperature spring in fuel cell stack, anode off-gas recirculation rate, air inlet temperature and external pre-reforming reaction extent is analyzed. The present study revealed to be a powerful tool for evaluating the SOFC system performance under a wide range of operation and paves the way for defining control strategies in order to maintain high system efficiency under part-load operations.     

Three‐Dimensional Computational Fluid Dynamics Modeling of a Planar Solid Oxide Fuel Cell

A three‐dimensional computational fluid dynamics model was developed to study the performance of a planar solid oxide fuel cell (SOFC). The governing equations were solved with the finite volume method. The model was validated by comparing the simulation results with data from literature. Parametric simulations were performed to investigate the coupled heat/mass transfer and electrochemical reactions in a planar SOFC. Different from previous two‐dimensional studies the present three‐dimensional analyses revealed that the current density was higher at the center along the flow channel while lower under the interconnect ribs, due to slower diffusion of gas species under the ribs. The effects of inlet gas flow rate and electrode porosity on SOFC performance were examined as well. The analyses provide a better understanding of the working mechanisms of SOFCs. The model can serve as a useful tool for SOFC design optimization.     

Effect of Creep of Ferritic Interconnect on Long‐Term Performance of Solid Oxide Fuel Cell Stacks

High‐temperature ferritic alloys are potential candidates as interconnect (IC) materials and spacers due to their low cost and coefficient of thermal expansion (CTE) compatibility with other components for most of the solid oxide fuel cells (SOFCs). However, creep deformation becomes relevant for a material when the operating temperature exceeds or even is less than half of its melting temperature (in degrees of Kelvin). The operating temperatures for most of the SOFCs under development are around 1,073 K. With around 1,800 K of the melting temperature for most stainless steel (SS), possible creep deformation of ferritic IC under the typical cell operating temperature should not be neglected. In this paper, the effects of IC creep behaviour on stack geometry change and the stress redistribution of different cell components are predicted and summarised. The goal of the study is to investigate the performance of the fuel cell stack by obtaining the changes in fuel‐ and air‐channel geometry due to creep of the ferritic SS IC, therefore indicating possible changes in SOFC performance under long‐term operations. The ferritic IC creep model was incorporated into software SOFC‐MP and Mentat‐FC, and finite element analyses (FEAs) were performed to quantify the deformed configuration of the SOFC stack under the long‐term steady‐state operating temperature. It was found that the creep behaviour of the ferritic SS IC contributes to narrowing of both the fuel‐ and the air‐flow channels. In addition, stress re‐distribution of the cell components suggests the need for a compliant sealing material that also relaxes at operating temperature.     

Polarization characteristics and fuel utilization in anode-supported solid oxide fuel cell using three-dimensional simulation

A three-dimensional numerical simulation for anode-supported tubular solid oxide fuel cell (SOFC), which is characterized by good electrical conductivity, has been carried out. Performance results by simulation are in good agreement with those by experiments, reported in [7]. Effect of various process conditions such as operating temperature, inlet velocity of fuel, and flow direction of inlet gases on the cell performance and fuel utilization has been further scrutinized. Polarization curve rises with increasing temperature of preheated gases and chamber, resulting from the incremented activity of catalysts within electrode. An effective way to reduce the temperature variation in the single cell with increasing current density has been sought, considering the temperature-dependent thermal expansion of materials. It has also been found that the fuel utilization is enhanced by increasing the cell length and operating temperature and lowering the inlet velocity of fuel.     

Design and Fabrication of a Novel Electrode-Supported Honeycomb SOFC

We report the design and fabrication of a novel electrode-supported honeycomb solid oxide fuel cell (SOFC), that can generate high volumetric power density. Among various cell designs, honeycomb SOFCs are suitable for compact SOFC modules because they have a large surface electrode area per unit volume. We have succeeded in fabricating a cathode-supported honeycomb SOFC via extrusion of a LaSrMnO₃ honeycomb monolith and through the use of a new slurry injection method for the channel surface coating using electrolyte/anode bi-layers. The fabricated honeycomb SOFCs exhibited high volumetric power densities of approximately 1.2 W/cm³ at 600°C under a wet H₂ fuel flow.     

A Mathematical Model of SOFC: A Proposal

The mathematical model of the solid oxide fuel cell (SOFC) is presented. The new approach for modeling the voltage of SOFC is proposed. Electrochemical, thermal, electrical, and flow parameters are collected in the 0D mathematical model. The aim was to combine all cell working conditions in as a low number of factors as possible and to have the factors relatively easy to determine. A validation process for various experimental data was made and adequate results are shown. The presented model was validated for various fuel mixtures in relatively wide ranges of parameters as well as for various cell design parameters (e.g. electrolyte thickness, anode porosity, etc.). A distinction is made between the “design‐point” and “off‐design operation”.     

The transient operation of a solid oxide fuel cell monolith under forced periodic reversal of the flow

The forced periodic reversal of the flow is proposed for the case of a Solid Oxide Fuel Cell (SOFC) monolith. A one-dimensional non-steady state heterogeneous model is applied to an investigation of H₂ electrochemical oxidation in a co-current flow solid oxide monolithic fuel cell. Results are reported on the transient evolution along the reactor, of the species conversion, temperature distribution, thermodynamic energy conversion efficiency and volumetric power density. This novel transient operation of an SOFC leads to improved and highly efficient performances, thus allowing for a combination of the concepts of a regenerative heat preheater and of an electrocatalytic converter, in a single SOFC monolithic assembly.     

Steady-state multiplicity in a solid oxide fuel cell: Practical considerations

Steady-state multiplicity in a solid oxide fuel cell (SOFC) in three modes of operation, constant ohmic external load, potentiostatic and galvanostatic, is studied using a detailed first-principles lumped model. The SOFC model is derived by accounting for heat and mass transfer as well as electrochemical processes taking place inside the fuel cell. Conditions under which the fuel cell exhibits steady state multiplicity are determined. The effects of operating conditions such as convection heat transfer coefficient and inlet fuel and air temperatures and velocities on the steady state multiplicity regions are studied. Depending on the operating conditions, the cell exhibits one or three steady states. For example, it has three steady states: (a) at low external load resistance values in constant ohmic external load operation and (b) at low cell voltage in potentiostatic operation.     

Modelling and Performance Evaluation of Solid Oxide Fuel Cell for Building Integrated Co‐ and Polygeneration

Models of fuel cell based combined heat and power systems, used in building energy performance simulation codes, are often based on simple black or grey box models. To model a specific device, input data from experiments are often required for calibration. This paper presents an approach for the theoretical derivation of such data. A generic solid oxide fuel cell (SOFC) system model is described that is specifically developed for the evaluation of building integrated co‐ or polygeneration. First, a detailed computational cell model is developed for a planar SOFC and validated with available numerical and experimental data for intermediate and high temperature SOFCs with internal reforming (IT‐DIR and HT‐DIR). Results of sensitivity analyses on fuel utilisation and air excess ratio are given. Second, the cell model is extended to the stack model, considering stack pressure losses and the radiative heat transfer effect from the stack to the air flow. Third, two system designs based on the IT‐DIR and HT‐DIR SOFCs are modelled. Electric and CHP efficiencies are given for the two systems, as well as performance characteristics, to be used in simulations of building integrated co‐ and polygeneration systems.     

Enhancing the Efficiency of SOFC‐Based Auxiliary Power Units by Intermediate Methanation

Fuel‐cell‐based auxiliary power units benefit from the high power density and fuel flexibility of solid oxide fuel cells (SOFCs), facilitating straightforward onboard fuel processing of diesel or jet fuel. The preferred method of producing the fuel gas is autothermal reforming, which to date has shown the best practical applicability. However, the resulting reformate is poor in methane, so that cell cooling is not supported by internal methane steam reforming. Accordingly, large flow rates of excess air are required to cool the stack. Hence, the power demand of the cathode air blower significantly limits the net electrical power output of the system and large cathode flow channels are required. The present work examines attempts to further increase the system efficiency in middle‐distillate‐fueled SOFC systems by decreasing the cathode air flow rates. The proposed concept is generally based on inducing endothermic methane steam reforming (MSR) inside the cells by augmenting the methane content in an upstream methanation step. Methanation, however, can only yield significant methane production rates if the reaction temperature is limited. Therefore, four process layouts are presented that include different cooling measures. Based on these setups, the general feasibility and the benefit of intermediate methanation are demonstrated.     

Simultaneous measurement of current and temperature distributions in a proton exchange membrane fuel cell during cold start processes

Cold start is critical to the commercialization of proton exchange membrane fuel cell (PEMFC) in automotive applications. Dynamic distributions of current and temperature in PEMFC during various cold start processes determine the cold start characteristics, and are required for the optimization of design and operational strategy. This study focuses on an investigation of the cold start characteristics of a PEMFC through the simultaneous measurements of current and temperature distributions. An analytical model for quick estimate of purging duration is also developed. During the failed cold start process, the highest current density is initially near the inlet region of the flow channels, then it moves downstream, reaching the outlet region eventually. Almost half of the cell current is produced in the inlet region before the cell current peaks, and the region around the middle of the cell has the best survivability. These two regions are therefore more important than other regions for successful cold start through design and operational strategy, such as reducing the ice formation and enhancing the heat generation in these two regions. The evolution of the overall current density distribution over time remains similar during the successful cold start process; the current density is the highest near the flow channel inlets and generally decreases along the flow direction. For both the failed and the successful cold start processes, the highest temperature is initially in the flow channel inlet region, and is then around the middle of the cell after the overall peak current density is reached. The ice melting and liquid formation during the successful cold start process have negligible influence on the general current and temperature distributions.     

Numerical Investigation into Thermofluidic and Electrochemical Characteristics of Tubular‐type SOFC

Three‐dimensional simulations based on a multi‐physics model are performed to examine the thermofluidic and electrochemical characteristics of a tubular, anode‐supported solid oxide fuel cell (SOFC). The simulations focus on the local transport characteristics of the cathode and anode gases and the distribution of the temperature field within the fuel cell. In addition, the electrochemical properties of the SOFC are systematically examined for a representative range of inlet gas temperatures and pressures. The validity of the numerical model is confirmed by comparing the results obtained for the correlation between the power density and the current density with the experimental results presented in the literature. Overall, the present results show that the performance of the tubular SOFC is significantly improved under pressurised conditions and a higher operating temperature.     

High-performance microfluidic vanadium redox fuel cell

We demonstrate a new microfluidic fuel cell design with high-surface area porous carbon electrodes and high aspect ratio channel, using soluble vanadium redox species as fuel and oxidant. The device exhibits a peak power density of 70 mW cm⁻² at room temperature. In addition, low flow rate operation is demonstrated and single pass fuel utilization levels up to 55% are achieved. The proposed design facilitates cost-effective and rapid fabrication, and would be applicable to most microfluidic fuel cell architectures.